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13 November 2003 CRISP contourlets: a critically sampled directional multiresolution image representation
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Abstract
Directional multiresolution image representations have lately attracted much attention. A number of new systems, such as the curvelet transform and the more recent contourlet transform, have been proposed. A common issue of these transforms is the redundancy in representation, an undesirable feature for certain applications (e.g. compression). Though some critically sampled transforms have also been proposed in the past, they can only provide limited directionality or limited flexibility in the frequency decomposition. In this paper, we propose a filter bank structure achieving a nonredundant multiresolution and multidirectional expansion of images. It can be seen as a critically sampled version of the original contourlet transform (hence the name CRISP-contourets) in the sense that the corresponding frequency decomposition is similar to that of contourlets, which divides the whole spectrum both angularly and radially. However, instead of performing the multiscale and directional decomposition steps separately as is done in contourlets, the key idea here is to use a combined iterated nonseparable filter bank for both steps. Aside from critical sampling, the proposed transform possesses other useful properties including perfect reconstruction, flexible configuration of the number of directions at each scale, and an efficient tree-structured implementation.
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Yue Lu and Minh N. Do "CRISP contourlets: a critically sampled directional multiresolution image representation", Proc. SPIE 5207, Wavelets: Applications in Signal and Image Processing X, (13 November 2003); https://doi.org/10.1117/12.506566
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